This is a very common problem with Dodge Neon cars. They flood in the back seats big time. I had this problem with 1998 Dode Neon (manual), then bough 2000 Neon. Inititially it did not flood at all but now it does. I searched the forms, could not find a solution anywhere. Does anyone know why Neons flood with water in rain?
I wish you luck. In my experience any car that's 10 years old or more is probably leaking somewhere, just most times people haven't noticed yet (although, they eventually notice when the floor rusts through and falls out). The causes of leaks are multitude. You just have to go around every spot where there's a break in the metal (antennas, windows, trim, handles, gas doors, etc.) and inspect carefully/hose down while watching for water...
The flooding problem is probably the funky gaskets used around the tail lights. Get some silicone, take the tail light assembly off and on the left side run a bead of silicone. The water runs down the trunk track right along the left side of the gasket and ruins it's properties over time. The gaskets cost around $12.00 on ebay but from what I've read online in other forums, the lifespan isn't much over 5 years before they start leaking again.
You'll want to check the spare tire well also. Mine had 4 inches of water in it prior to sealing the leaky spot with silicone.
There is also another leak very common on Dodge Neons, and that is in the front under the dash. If the AC condensation overflow hose gets plugged it will send all that water down the inside of the firewall, along whatever wires it comes into contact with, shorting out your CD player and radio and filling the passenger side floorboards with water. To fix that, take an airhose, stuff it into the drain hose and shoot a few short bursts of air into it. If it is plugged you will have Niagara flowing within seconds.
Hope this helps someone.